Sorry to see that no one has answered your inquiry yet... There are
other folks out there who will probably have more to say on this, but
here's some info:

One thing that has been fascinating me is the fact that our
perception of underwater sound is realized through bone conduction.

I don't know that for sure, but it seems plausible - what are your
sources for this?

For what I could gather by relating different sources is that when
inside water the impedance matching/communication from the ear drum
(air) to the inner ear (fluid) through the ossicles is stopped. As
a result our air conducted listening is also stopped.

The middle ear has apparently evolved to reduce the impedance
mismatch between the air in the ear canal and the liquid-filled inner
ear. When the head is immersed, there's another water-air interface
in the ear canal (I think that the ear canal doesn't fill with water,
so there's a bubble near the eardrum), so there's another impedance
mismatch there without any mechanism to compensate for it, and sound
transmission through the ear canal is reduced.

On the other hand, the impedance mismatch between the surface of the
skull and the surrounding fluid (air or water) is reduced when the
head is immersed, since water has a much higher specific impedance
than air. In air, sound transmission through the head is 40-60 dB
lower than through the ear canal; in water, sound transmission
through the head is likely to be considerably higher and may be
higher than through the ear canal.

Another factor is that, at least at low frequencies, sound perceived
by "bone conduction" is conducted through the head to the ear canal
and (apparently) causes the ear canal wall to vibrate, setting up a
sound signal in the ear canal near the eardrum that is conducted to
the cochlea in the usual fashion. At higher frequencies, other
mechanisms seem to be dominant. (See Shyam Khanna's work for this -
ref. below.)

And of course sound can be conducted to the head through the body. A
paper we put out a few years ago suggests that the body-conduction
mechanism is less efficient than conduction through the head, but not
by a lot. The old "Bone-Fone" loudspeakers worked this way - you'd
wear them draped over your shoulders. (I never tried them out though.)

David Mountain and Darlene Ketten have done a lot of work, especially
recently, on hearing and sound conduction in marine mammals - you
might look up some of their recent papers (and maybe this post will
spur them to weigh in).

And it raises the question: How well do people with a conductive
hearing loss hear underwater? Is their hearing underwater comparable
to that of normal-hearing people?